When you said you had errors all over the place I immediately thought of corrupted memory because I had experienced the very same issues. Then I read your minidumps:

The first is an 0x7F error: UNEXPECTED_KERNEL_MODE_TRAP
One of three types of problems occurred in kernel-mode: (1) Hardware failures. (2) Software problems. (3) A bound trap (i.e., a condition that the kernel is not allowed to have or intercept). Hardware failures are the most common cause and, of these, memory hardware failures are the most common.

You also had an 0x24 error: NTFS_FILE_SYSTEM. There are a lot of causes for this error. From auhma.org -

A problem occurred within NTFS.SYS, the driver file that allows the system to read and write to NTFS file system drives.

a.) There may be a physical problem with the disk, or an Interrupt Request Packet (IRP) may be corrupted.

b) Other common causes include heavy hard drive fragmentation, heavy file I/O, problems with some types of drive-mirroring software, or some antivirus software.

c) They suggest suggest running ChkDsk or ScanDisk as a first step; then disable all file system filters such as virus scanners, firewall software, or backup utilities.

d) Check the file properties of NTFS.SYS to ensure it matches the current OS or SP version.

e) Update all disk, tape backup, CD-ROM, or removable device drivers to the most current versions.

* Not only would I run chkdsk but I would also run a full harddrive diagnostics that you can for free from your harddrive manufacturer's website.

* Run MemTest on your RAM for a minimum of 7 passes. if you have any errors you have corrupted memory that needs to be replaced.